They're both really awesome games and if you can I would recommend getting both. But if I HAD to chose only one then it would be Etrian Odyssey IV. It's my favorite game for the 3DS and I've spent way more time on it than FEA so IMO it's more bang for you're buck. I've spent 96 hours on it and still haven't beaten it just to give you an idea. On my gaming long EO4 is #1 while FEA was #2 up until recently (animal crossing took the #2 spot lol), so yeah they're both awesome games and I absolutely love them both. But once again my recommendation would be for EO4.

Since you clearly seem to enjoy playing Etrian Odyssey IV so much, and that demo is pretty accurate representation of how the full game plays (FE:A's is rather threadbare, by comparison), I'd recommend getting EOIV first. Better to buy something you know you'll love over something you might love, imo

I found Fire Emblem to be the better game. I can tell you that it shouldn't be judged by the demo alone. Etrian Odyssey, meanwhile, gives quite a bit of play value for the demo, so it gives you a better idea of how the game is.

I'd recommend Fire Emblem, but really, you can't go wrong. They're both fantastic games with tons of content.

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Gonna have to agree with pretty much everyone else here: eventually you're probably gonna want to get both. I haven't actually played EO4 yet (live in Europe), but based on my experience with the previous games, which are awesome, and the fact that you liked the demo, I'd recommend getting that first.

I didn't love the FE demo either but trust me, the more you play, the better it gets. I think a big part of the satisfaction comes from watching your characters grow and learning to exploit the terrain and combat system to your advantage. The game gets more exciting when more complicated mechanics come into play imo.

Be advised that Etrian (or at least in my experience with 2 and 3) has a honeymoon period, after which, the repetitive nature of the game might start to test you patience a little. I just take a break every now and then.

Yeah definitely get both. Personally I say Etrian Odyssey IV but so far maybe Shin Megami Tensei IV. Etrian Odyssey IV had just such a satisfying basis, you get to explore, push new boundaries, and draw the maps you will use. The QR quests were interesting and very fun for them to do!